Finding magnitude and direction of net force on a dipole.

In summary, the dipole has a net force of +q on it in the limit x >> a due to the charges being equidistant and having opposite signs.
  • #1
jlmccart03
175
9

Homework Statement


A dipole with charges ±q and separation 2a is located a distance x from a point charge +Q, oriented as shown in the figure.

Part A:
Find an expression for the magnitude of the net force on the dipole in the limit x≫a.

Part B:
What is the direction of the net force? Enter answer as number of degrees counterclockwise from the positive x-direction.
upload_2017-1-30_18-13-15.png


Homework Equations


F = kq1q2/r2

The Attempt at a Solution


I honestly cannot think of a solution for this problem. Currently I am stuck on the dipole piece. How does one come up with an equation using the limit x >> a? I guess a better question would be what that means in terms of figuring out the net Force on the dipole. I am simply confused on where to start or how to begin besides using F = kq1q2/r2
 
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  • #2
jlmccart03 said:
F = kq1q2/r2
Mostly, students start with an equation they have learned specifically related to dipoles. I cannot tell whether you are expected to start from there or from the equation you quoted. Either will do, but it is a bit more work using the latter. Since that's the equation you quote, I'll assume for now that is the method to use.

If you were asked to find the force the dipole exerts on the point charge, could you do that?
 
  • #3
haruspex said:
Mostly, students start with an equation they have learned specifically related to dipoles. I cannot tell whether you are expected to start from there or from the equation you quoted. Either will do, but it is a bit more work using the latter. Since that's the equation you quote, I'll assume for now that is the method to use.

If you were asked to find the force the dipole exerts on the point charge, could you do that?
Well the dipole exerts both a positive and negative force onto the +Q charge which would simply cancel out correct? Since they are equidistant thus equal, but opposite magnitudes.
 
  • #4
jlmccart03 said:
Well the dipole exerts both a positive and negative force onto the +Q charge which would simply cancel out correct? Since they are equidistant thus equal, but opposite magnitudes.
The two forces are not quite in the same direction, so they do not quite cancel. It's the little bit of force remaining that is of interest.
 
  • #5
The diagram might make you think the charge is spread out over the dipole, but when they say separated by 2a they are telling you to treat them as point charges.

Treat the dipole as a rigid body in two dimensions. It has two forces acting on it. Draw a free body diagram, resolve the forces into their components, write the net force components and see if it approximates to something simpler as x becomes much larger than a.
 

1. What is a dipole?

A dipole is a molecule or object that has two equal and opposite charges separated by a distance. This creates a positive end and a negative end, which gives the dipole its polarity.

2. How do you calculate the magnitude of net force on a dipole?

The magnitude of net force on a dipole can be calculated using the formula F = qEsinθ, where q is the magnitude of the charge on the dipole, E is the strength of the electric field, and θ is the angle between the dipole moment and the electric field.

3. What is the direction of the net force on a dipole?

The direction of the net force on a dipole is always towards the stronger end of the dipole. This means that the positive end is pulled towards the negative end of the dipole, and vice versa.

4. How does the distance between the charges on a dipole affect the net force?

The closer the charges are to each other, the stronger the net force will be. This is because the electric field is stronger when the charges are closer together, increasing the force experienced by the dipole.

5. Can a dipole experience a net force in a uniform electric field?

Yes, a dipole can experience a net force in a uniform electric field. This is because even though the electric field is uniform, the dipole has a polarity and will experience a force towards the stronger end of the dipole.

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